Measure space

Before we can define Measure space we need a Measurable space.

Measure space

A Measurable space $(X,\mathcal{A})$ and a function, $$\mu:\mathcal{A}\rightarrow[0,\infty]$$ which is a measure is a measure space, that is a measure space is:

$$(X,\mathcal{A},\mu:\mathcal{A}\rightarrow[0,\infty])$$ but recall mathematicians are lazy so we just write $$(X,\mathcal{A},\mu)$$